A certain amount of NaOH is dissolved in certain kilograms of solvent and molality of the solution is 0.5 m. When the same amount of NaOH is dissolved in 100 grams of less solvent than initial then molality becomes 0.625 m. Determine the amount of NaOH and the initial mass of solvent.​

NaOH is dissolved in certain kilograms of solvent and molality of solution 0.5m.

Again , same among of NaOH is dissolved in 100 grams of solvent than initial , then molality becomes 0.625m.

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Now lets find the amount of NaOH and the initial mass of solvent.

Let,

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$\sf\bold{ ❍ We\:know,}$

$\sf{Molality(m)=}$ $\sf\dfrac{No.of\:moles\:of\:solute}{No.of\:solvent\:in\:kg}$

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$\sf\bold{Putting\:the\:formula:-}$

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$\sf\huge\underline\bold{ ❍Case:1}$

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$\longmapsto$ $\sf\small{0.5}$ $\sf\dfrac{x}{y}$

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$\longmapsto$ $\sf{0.5y = x }$

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$\longmapsto$ $\sf{multiply\:by\:2→ y = 2x}$

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$\sf\huge\underline\bold{ ❍Case:2}$

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$\longmapsto$ $\sf\small{0.625}$ $\sf\small\dfrac{x}{y}$ = $\sf\dfrac{x}{y=100g}$

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$\longmapsto$ $\sf\small{0.625}$ $\sf\dfrac{x}{y-100/1000kg}$ = $\sf\dfrac{x}{y-0.1kg}$

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$\longmapsto$ $\sf{0.625(y-0.1kg)=x}$

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$\longmapsto$ $\sf{0.625y-0.0625=x}$

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$\sf\small\bold{By\:putting\:the\:value\:of \:"x" we\: get:}$

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$\longmapsto$ $\sf{0.625(2x)-0.0625 = x}$

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$\longmapsto$ $\sf{1.25x 0.0625 = x}$

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$\longmapsto$ $\sf{1.25x - x = 0.0625}$

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$\longmapsto$ $\sf{0.25x = = 0.0625}$

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$\longmapsto$ $\sf\small{x=}$ $\sf\dfrac{0.0625}{0.25}$= $\sf\bold{x=0.25}$

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$\sf{So,y=2(x)=2\times0.25=}$ $\sf\bold{y=0.5}$

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$\sf\small{Initial\:mass\:of\:solvent:0.5kg=500g}$

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$\sf{Now,}$

Amount of NaOH=

$\space$ $\space$ $\space$ $\space$ $\space$ $\sf{=x\times molar\:mass}$

$\space$ $\space$ $\space$ $\space$ $\space$ $\sf{=0.25\times 40=10}$

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$\sf\underline{\underline{ ⚘ Hence,amount\:of\:NaOH=10kg}}$

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"you start with 15.67 g mgco3-xh2o, when heated and all the water is removed, you are left with 7.58 g mgco3 only.

therefore, you had 15.67 - 7.58 = 8.09g h2o  

moles of each :

7.58g mgco3 = ? moles = 7.58g / 83.4g/mole = 0.09moles  

8 09g h2o = ? moles = 8.09g / 18g/mole = 0.44moles  

molar ratio between the two by dividing both numbers by the smallest number :

0.09 / 0.09 = 1  

0.44 / 0.09 = 4.8  

mgco3-5h2o"

pre-sliced bread is a relatively recent development in baking technology. previous to that, it was always sold in a bakery in daily-made contiguous loaves with no wrapping, and was moderately perishable, usually being used with a day or two (which is why every bakery had a discounted “day-old” bread table.) therefore, pre-sliced bread would grow stale quickly. the hard crust provided a protective layer, and once the exposed dry slice left from the previous cut was removed, the interior was still soft.

what keeps bread soft is the moisture retained in the crumb (the light spongy part that’s not crust). the reason the crust develops is the surface of the dough gets exposed to hot dry air during baking which browns the outer layer and seals it, preventing all the moisture from escaping the dough. longer exposure to air will also eventually cause your bread to lose flavor and become stale.

people were used to cutting slices as they needed them and storing bread in a specially-made wooden or metal breadbox or pail with a lid to preserve it longer, but the first automatically sliced commercial loaves were produced on july 6, 1928, in chillicothe, missouri, using a machine invented by otto rohwedder, an iowa-born, missouri-based jeweler.[1] pre-sliced bread would indeed dry out, were it not for another 20th century technology: the plastic bag. bread could now be pre-sliced, and if the enclosing bag remains sealed as much as possible, the bread will remain soft and fresh for longer than if sitting unwrapped on a shelf or enclosed in a bread box that is not air-tight. sealed packaging meant bread could also be sold on store shelves and eliminate frequent trips to a bakery.

sealing bread in a plastic bag had another effect: the moisture in the loaf will re-distribute into the crust and soften it, which is sometimes more pleasing in a sandwich - especially for children whose teeth might not yet be strong enough to tear through a hard crust. a homemade loaf of bread can be sealed in a bag overnight and the crust will become soft like store-bought sandwich bread.

these were novel changes in how bread was produced and sold, which led to the coining of the phrase “the greatest thing since sliced bread.”